Question

Using the 32-bit binary representation for floating point numbers, represent the number 10111001100112 as a 32...

Using the 32-bit binary representation for floating point numbers, represent the
number 10111001100112 as a 32 bit floating point number.

Homework Answers

Answer #1

01000101101110011001100000000000

Explanation:
-------------
1011100110011 => 1.011100110011 * 2^12

single precision:
--------------------
sign bit is 0(+ve)
exponent bits are (127+12=139) => 10001011
   Divide 139 successively by 2 until the quotient is 0
      > 139/2 = 69, remainder is 1
      > 69/2 = 34, remainder is 1
      > 34/2 = 17, remainder is 0
      > 17/2 = 8, remainder is 1
      > 8/2 = 4, remainder is 0
      > 4/2 = 2, remainder is 0
      > 2/2 = 1, remainder is 0
      > 1/2 = 0, remainder is 1
   Read remainders from the bottom to top as 10001011
   So, 139 of decimal is 10001011 in binary
frac/significant bits are 01110011001100000000000

so, 1011100110011_2 in single-precision format is 0 10001011 01110011001100000000000
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